Piston $—$ Simple piston

This is a model of a piston.

 Equations $0=f\mathrm{switch}+{f}_{A}+{f}_{B}$ $0=-f\mathrm{switch}+{f}_{A\left(\mathrm{support}\right)}+{f}_{B\left(\mathrm{support}\right)}$ $\mathrm{\rho }={\mathrm{\rho }}_{\mathrm{oil}}\left({p}_{\mathrm{abs}}={p}_{\mathrm{abs}},T=T,{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right)$ $T={T}_{0\left(\mathrm{oil}\right)}+{\mathrm{ΔT}}_{\mathrm{system}}$ $V=A\mathrm{switch}{s}_{a\left(\mathrm{rel}\right)}+{V}_{0}$ $f=Ap$ $p={p}_{A}$ ${V}_{A}=V$ ${s}_{a\left(\mathrm{rel}\right)}={s}_{A}-{s}_{A\left(\mathrm{support}\right)}$ ${m}_{\mathrm{flow}\left(A\right)}=0$ ${s}_{\mathrm{ab}\left(\mathrm{rel}\right)}={\ell }_{\mathrm{piston}}$ ${s}_{\mathrm{ab}\left(\mathrm{rel}\right)}=\mathrm{switch}\left({s}_{B}-{s}_{A}\right)$ ${s}_{B\left(\mathrm{support}\right)}=L\mathrm{switch}+{s}_{A\left(\mathrm{support}\right)}$ ${p}_{\mathrm{abs}}=p+{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}$

Variables

 Name Value Units Description Modelica ID ${{s}_{\mathrm{rel}}}_{a}$ $m$ Relative position of flangeA wrt supportA s_rel_a ${{s}_{\mathrm{rel}}}_{\mathrm{ab}}$ $m$ Relative position of flangeB wrt flangeA s_rel_ab $f$ $N$ Force acting in positive direction of flangeA f $V$ ${m}^{3}$ Volume V $T$ $K$ Temperature T $\mathrm{\rho }$ $\frac{\mathrm{kg}}{{m}^{3}}$ Density rho ${p}_{\mathrm{abs}}$ $\mathrm{Pa}$ Absolute pressure, used for all property calls p_abs $p$ $\mathrm{Pa}$ Gauge pressure p ${p}_{\mathrm{sat}}$ [1] $\mathrm{Pa}$ Gas saturation pressure p_sat

[1] $\mathrm{oil.gasSaturationPressure}\left(T=T,{v}_{\mathrm{gas}}={\mathrm{oil.v}}_{\mathrm{gas}}\right)$

Connections

 Name Description Modelica ID $\mathrm{supportA}$ supportA $\mathrm{supportB}$ supportB $\mathrm{flangeA}$ flangeA $\mathrm{flangeB}$ flangeB $\mathrm{oil}$ Fluid property model oil $\mathrm{portA}$ portA

Parameters

 Name Default Units Description Modelica ID $L$ $m$ Element length L $\mathrm{reverse}$ $\mathrm{false}$ Reverse the sign convention, see documentation for details reverse $\mathrm{switch}$ $\left\{\begin{array}{cc}-1& \mathrm{reverse}=\mathrm{true}\\ 1& \mathrm{otherwise}\end{array}\right\$ -1 if reverse, else 1 switch ${V}_{0}$ $0$ ${m}^{3}$ Dead volume V0 $A$ ${m}^{2}$ Working area A ${\ell }_{\mathrm{piston}}$ $L$ $m$ Piston length l_piston ${\mathrm{ΔT}}_{\mathrm{system}}$ $0$ $K$ Temperature offset from system temperature dT_system